Latest Elitmus Aptitude Question SOLUTION: 100^x (log x (base 3) - log sqrt x (base 9))... X is Always greater than 1 Option a) 0, infinity b) -infinity, infinity c) infinity, -infinity d) None

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(#M40035006) ELITMUS Numerical Ability question Logrithm Keep an EYE

100^x (log x (base 3) - log sqrt x (base 9))... X is Always greater than 1
Option
a) 0, infinity
b) -infinity, infinity
c) infinity, -infinity
d) None

Asked In Elitmus tausif (10 years ago)

Unsolved Read Solution (4)

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Read Solution (4) :

RAKESH  (10 years ago)

it should be right

100^x (log x (base 3) - log sqrt x (base 9))

= 100^x (log x (base 3) - log x^(1/2) (base 3^2))

= 100^x (log x (base 3) - (1/4)*log x (base 3))

= 100^x *(3/4)*log x (base 3)

as x > 1
log x (base 3) is always +ve , so given exp always +ve & never equal to zero or -infinity. as x inc, value of given exp tends to infinity.

so, 100^x (log3 basex - log root9 basex) lies in interval ( 0, infinity)

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Abhishek Jha  (10 years ago)

Let 3^a = x, then 9^(a/2) = x.
Taking square root from both sides we get, (9^a/2)^1/2 = sqrt(x),
=> 9^(a/4) = srt(x).
So, log of sqrt(x) to the base 9 will be a/4.

Now the given expression will evaluate to 100^x(a - a/4) = 100^x * 3a/4.
As x is greater than 1, and we have 3^a = x, and as 3^0 = 1, a will always be greater than 0.
Also, as a ->0, expr. ->0 and as a->infinity, expr. ->infinity.
So, the required range will be (a) 0, infinity.

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RAKESH  (10 years ago)

100^x(log 9 base x - log root3 base x)

= 100^x(log 3^2 base x - log 3^(1/2) base x)

= 100^x(2*log3 base x - (1/2) *log3 base x)

100^x(3/2)*log3 base x

as x > 1
for any values of x, given exp is always +ve, it is never equal to zero or -Infinity.as x inc, value of given exp tends to infinty.

value of 100^x (log3 basex - log root9 basex) lies in interval (0, infinity)

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rohitashwa  (10 years ago)

@rakesh where I am doing a mistake?? help!!!!
100^x(log x(base 3)-log sqrt x(base 3^2)
= 100^x(log x(base 3)-1/4 log x base3
=100^x((log x(base 3)-1/4 log x(base 3))
=100^x((3/4 log x(base 3))
=now as x=>-3 we get -ve values...while x>=3 +ve

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